Question: Does ADS-B as a concept require GPS to work?
Answer: No.
The D in "ADS-B" stands for dependent, as in, on onboard navigation sources. Now what exactly the technology of that source is is fully open for implementation to resolve - it doesn't say "dependent on GNSS". It just so happens that GPS is currently the only such system out there that delivers the accuracy, integrity and continuity needed to make the dependency worthwhile for surveillance application in civil aviation. So what are other navigation sources that could be considered?
In the first instance, generally any GNSS. Technically, the russian GLONASS is good enough for the same application as GPS and using or not using it for ADS-B is a political question. Putin loves nothing more than to lure gullible and shortsighted west European politicians into yet more interdependency so that he can then force their hand when needed, like, say, when invading a neighbour country with aspirations towards membership in Euro or North Atlantic institutions. Soon enough China will have their version of GNSS running and India is aspiring to the same at a longer horizon. In the ADS-B standard there is nothing that forbides the respective countries to enable, or dare I say, mandate that traffic operating in their airspace be ADS-B capable using their native GNSS system. It is the likelihood of an equivalent reciprocation from the West that makes this a non-option, not the technical means.
In the second instance, the onboard inertial unit. Contemporary systems, albeit improving, generally are not yet up to the performance standards required for proper surveillance but it is better than nothing if the GPS should fail or become unavailable, and position info delivered by those is useful in degrading to procedural control or clearing the sky, whatever is stipulated as the next mode of operation. It may not be usable to provide a 5NM separation due to low integrity, but it is still usable information.
And in third and further instances, any number of technological means, extant or upcoming. Take a look in the NAV domain, where PBN makes good use of the existing DME infrastructure, to great effect. A pair of DME's in a suitable configuration can support a 0.3 NM RNP approach - that is way more precise than what a 5 NM enroute separation would require. It would however by prohibitively expensive to dot the Earth with DME units to provide the required coverage for a meaningful separation application. Thus it becomes a feasibility limitation, but not a technical one.